Rule 4 of 36 · Chapter I — Measurement & Units
Know your orders of magnitude
Why this rule exists
Physical reasoning lives on a logarithmic scale: what matters first is not whether a quantity is 3 or 7, but whether it is 10⁻⁹ or 10³. Orders of magnitude let you compare things that differ by a factor of a trillion without drowning in digits, and they reveal which effects can be ignored outright. Knowing a few anchor values lets you locate any new quantity by interpolation, because most of physics spans a scaffold of powers of ten.
In practice
Memorize a handful of reference magnitudes: an atom is ~10⁻¹⁰ m, a proton mass ~10⁻²⁷ kg, Avogadro's number ~10²⁴, room-temperature thermal energy ~1/40 eV. To place a new quantity, express it in powers of ten and compare exponents; a difference of six powers means one effect is a million times the other and usually decides the problem. Track exponents first, digits later.
When it doesn't apply
Orders of magnitude blur distinctions that sometimes matter: a factor of 3 can be the whole point in a marginal engineering tolerance or a resonance. And two quantities sharing an order of magnitude may still differ enough that their competition, not their scale, sets the outcome.